The definition of start time in cancer treatment studies analysed by non-mixture cure models

Non-mixture cure models are derived from a simplified representation of the biological process that takes place after treatment for cancer. These models are intended to represent the time from the end of treatment to the time of first recurrence of the cancer in studies when a proportion of those treated are completely cured. However, for many studies, other start times are more relevant. In a clinical trial, it may be more natural to model the time from randomisation rather than the time from the end of treatment and in an epidemiological study, the time from diagnosis might be more meaningful. Some simulations and two real studies of childhood cancer are presented to show that starting from time of diagnosis or randomisation can affect the estimates of the cure fraction. The susceptibility of different parametric kernels to errors caused by using start times other than the end of treatment is also assessed. Analysing failures on treatment and relapse after completing the treatment as two processes offers a simple way of overcoming many of these problems.